Johnny Depp Engaged to Amber Heard
01/17/2014 AT 07:00 PM EST
"Of course they couldn't be happier to be engaged and excited to share the rest of their lives together," a source tells PEOPLE, adding that Heard has "told close friends" the news.
"Amber has really taken well to the kids and really enjoys spending time with them. And she's even taken Lily shopping on her own for some bonding time."
The couple, who met on the set of their 2011 movie The Rum Diary went public with their relationship the following year after Depp, 50, announced his split from partner of 14 years Vanessa Paradis.
He and the French actress and singer have two children, Lily-Rose, 14, and Jack, 11, but never married.
Heard, 27, who has said she's bisexual, was previously in a four-year relationship with Hawaiian artist and photographer Tasya van Ree.
The newly engaged couple are teaming up again on the big screen in the upcoming film London Fields, which stars Heard and features Depp in a cameo.
Reporting by JENNIFER GARCIA